Error Functions#
The error function is a special function related to the normal distribution.
- erf(x)#
Error function.
- Parameters:
x (Real) – The value to take the error function of.
- Definition:
\(\mathrm{erf}(x) = \dfrac{2}{\sqrt{\pi}} \displaystyle\int_0^x e^{-t^2} \, dt\)
- Domain:
\((-\infty, \infty)\)
- Range:
\((-1, 1)\)
- Returns:
The value of \(\mathrm{erf}(x)\).
- Return type:
Real
- erfc(x)#
Complementary error function.
- Parameters:
x (Real) – The value to take the complementary error function of.
- Definition:
\(\mathrm{erfc}(x) = 1 - \mathrm{erf}(x)\)
- Domain:
\((-\infty, \infty)\)
- Range:
\((0, 2)\)
- Returns:
The value of \(\mathrm{erfc}(x)\).
- Return type:
Real